If I'm reading this correctly it's two or threefold. Faster switching times, which both increases max speed and reduces power consumption. Avoids flaws due to silicon doping, presently we add ions to silicon to get P or N type junctions and they've found a way to get P type junctions using "2D Hole Gas" which is basically a thin layer of voids inside the bulk diamond crystal after treatment and avoids a category of flaws that affect silicon yields. Third, and this is speculation, but diamond has a way higher thermal conductivity and lower thermal expansion coefficient, so it can likely withstand higher temps and conduct heat away faster.
I think the better question is: what real world applications need these qualities enough to justify the cost? They mention cooling application, I don't buy that anyone is that interested in reducing hotspots in their chips even if it makes them last longer.